Correlation of Anxiety and Study Hours, Gender, and Sleep Patterns of DATA2002 Students

Figure 1. A student overwhelmed by study workload

1 Introduction

1.1 Addressing Questions

This report investigates how student lifestyle factors — including study habits, sleep patterns, and gender — relate to self-reported daily anxiety levels. As concerns about student mental health and academic pressure continue to grow, identifying behavioral correlates of anxiety is crucial for developing effective student support strategies within universities. This analysis seeks to explore meaningful patterns within student survey responses that may guide future academic and well-being interventions.

The dataset was collected via a voluntary and anonymous online survey distributed to students enrolled in the DATA2X02 unit at the University of Sydney. Although the sample might initially appear random due to the open participation format, it is in fact non-random, and several types of bias must be considered.

First, selection bias is likely present, as students who chose to participate may be more engaged, self-reflective, or motivated — characteristics that are not necessarily representative of the broader student population. As a result, variables such as self-reported anxiety, study hours, and approaches to assignment management may be systematically skewed.

Second, non-response bias must also be acknowledged. Students who chose not to complete the survey could differ in significant ways from respondents, especially in terms of sleep consistency, WAM, or assignment submission patterns, leading to distorted estimates of key outcomes.

Third, the dataset is subject to measurement bias, as many questions rely on self-reported data, which are vulnerable to social desirability effects and recall inaccuracies. This is particularly relevant for sensitive or subjective variables such as alcohol consumption, sleep hours, and daily anxiety levels.

To improve data quality in future iterations, certain survey items could be redesigned. For example, the question about daily anxiety (Q15) currently uses a simple 1–10 scale, but lacks defined anchors or examples, which may cause participants to interpret the scale inconsistently. Adding clearly labelled scale intervals (e.g., “1 = not at all anxious,” “10 = extremely anxious multiple times per day”) would reduce ambiguity.

Despite these limitations, the dataset remains suitable for exploratory statistical analysis. This report addresses three focused research questions using techniques from Modules 1 and 2, including parametric and non-parametric hypothesis testing, as well as resampling methods. Specifically, we examine how academic workload, gender, and sleep consistency are associated with daily self-reported anxiety.

1.2 Data Wrangling and Cleaning

library(tidyverse)
library(janitor)
library(hms)
library(ggplot2)
library(ggpubr)
library(lubridate)
theme_set(theme_bw())

x <- readxl::read_excel("DATA2x02_survey_2025_Responses.xlsx")
old_names = colnames(x)
new_names <- c(
  "timestamp",
  "target_grade",
  "assignment_preference",
  "trimester_or_semester",
  "age",
  "tendency_yes_or_no",
  "pay_rent",
  "stall_choice",
  "weetbix_count",
  "weekly_food_spend",
  "living_arrangements",
  "weekly_alcohol",
  "believe_in_aliens",
  "height",
  "commute",
  "daily_anxiety_frequency",
  "weekly_study_hours",
  "work_status",
  "social_media",
  "gender",
  "average_daily_sleep",
  "usual_bedtime",
  "sleep_schedule",
  "sibling_count",
  "allergy_count",
  "diet_style",
  "random_number",
  "favourite_number",
  "favourite_letter",
  "drivers_license",
  "relationship_status",
  "daily_short_video_time",
  "computer_os",
  "steak_preference",
  "dominant_hand",
  "enrolled_unit",
  "weekly_exercise_hours",
  "weekly_paid_work_hours",
  "assignments_on_time",
  "used_r_before",
  "team_role_type",
  "university_year",
  "favourite_anime",
  "fluent_languages",
  "readable_languages",
  "country_of_birth",
  "wam",
  "shoe_size",
  "books_read_highschool",
  "daily_water_intake_l",
  "perceived_old_age",
  "study_music_preference"
)
# overwrite the old names with the new names:
colnames(x) = new_names


df_clean <- x %>%
  select(
    daily_anxiety_frequency = 16,
    weekly_study_hours = 17,
    gender = 20,
    usual_bedtime = 22  
  ) %>%
  mutate(
    across(
      c(daily_anxiety_frequency, weekly_study_hours),
      ~ as.numeric(.)
    ),
    gender = str_to_lower(gender),
    gender = case_when(
      gender %in% c("female", "f", "girl", "girl ", "woman", "lady") ~ "Female",
      gender %in% c("male", "m", "man", "bloke", "guy") ~ "Male",
      gender %in% c("", "blank", NA) ~ NA_character_,
      TRUE ~ "Other"
    ),
    gender = factor(gender),
    usual_bedtime = as_hms(usual_bedtime),
    sleep_hour = hour(usual_bedtime)
  ) %>%
  drop_na(gender, daily_anxiety_frequency, weekly_study_hours, sleep_hour) %>%
  mutate(
    anxiety_group = case_when(
      daily_anxiety_frequency <= 3 ~ "Low",
      daily_anxiety_frequency <= 7 ~ "Mid",
      TRUE ~ "High"
    ),
    study_group = if_else(weekly_study_hours > 20, "> 20 hrs", "≤ 20 hrs")
  )

#table(df_clean$gender)
#glimpse(df_clean)

The calculations utilized in report were performed in R using the Rmarkdown environment to ensure reproducibility. Data Cleaning was carried out using various tidyverse packages. Column names were cleaned and shortened for clarity. Variables relevant to research was retained, including self-reported anxiety frequency, study hours, gender, and usual bedtime. Numeric variables were coerced into appropriate formats. Gender values were standardised for consistency into two groups, female and male since theand bedtime were converted to numeric hour values for further analysis.

2 Results

2.1 Does the distribution of anxiety levels differ by gender? (group the anxiety into groups: low, mid, high)

---

The bar chart in Figure 2 suggests that distribution of anxiety levels(low,mid,high) may differ across gender groups. To formally assess this, we performed chi-squared test of homogeneity to test whether the proportions of anxiety groups are same across different gender categories. Note that conducting a test of homogeneity, we assume that the responses were sampled independently from the student population that identify with each gender.

df_clean %>%
  select(gender, anxiety_group) %>%
  filter(gender != "Other") %>%
  drop_na() %>%
  ggplot(aes(x = gender)) +
  geom_bar(
    aes(fill = anxiety_group),
    position = "dodge",
    linewidth = 1
  ) +
  scale_fill_manual(values = c("Low" = "#9ecae1", "Mid" = "#fdd0a2", "High" = "#fc9272")) +
  labs(
    title = "Distribution of Anxiety Levels by Gender",
    x = "Gender",
    y = "Count",
    fill = "Anxiety Group"
  ) +
  theme_minimal(base_size = 13)

<Figure 2. Distribution of anxiety levels(Low, Mid, High) across gender groups>

tbl <- df_clean %>%
  filter(!is.na(gender), !is.na(anxiety_group)) %>%
  filter(gender != "Other") %>%
  count(gender, anxiety_group) %>%
  pivot_wider(names_from = anxiety_group, values_from = n, values_fill = 0) %>%
  column_to_rownames("gender") %>%
  as.matrix()

chisq.test(tbl)

    Pearson's Chi-squared test

data:  tbl
X-squared = 2.9237, df = 2, p-value = 0.2318

tbl

       High Low Mid
Female   33  31  65
Male     38  62 100

---

1. Hypothesis

• Null hypothesis (\(H_0\)):
  The proportions of anxiety levels(Low,Mid,High) are the same across gender groups(Female,Male, and Other).

• Alternative hypothesis (\(H_1\)):
  The proportions of anxiety levels differ for at least one gender group.

---

2. Assumptions

• The observations are independent(each student will contribute to only one gender group)

• Data are organized in contingency table and are categorical

---

3. Test Static

• Test type: Chi-squared test of homogeneity

• Test statistic (t): 2.9237

• Degrees of freedom (df): 2

---

4. P-Value

• Chi-squared approximation p-value: 0.2318

---

5. Decision

• Since the p-value is 0.2318, which is greater than 0.05(significance level), we fail to reject the null hypothesis. There is insufficient evidence to suggest that there are difference in anxiety level across gender groups.

---

6. Conclusion

• This result with Chi-squared test of homogeineity suggest that there are no statistically significant correlation between gender groups and daily anxiety levels in this sample. However, the presence of small counts in some cells(e.g: Other group) may limit the reliability of the test conducted, and larger sample may be needed to draw more firmer and rigor conclusions.

---

2.2 Do students who study more than 20 hours/week report lower anxiety levels than those who study less?

library(ggplot2)
library(ggpubr)
library(patchwork)

# A. Boxplot + jitter (study group vs anxiety)
p1 <- ggplot(df_clean, aes(x = study_group, y = daily_anxiety_frequency, fill = study_group)) +
  geom_boxplot(outlier.shape = NA, alpha = 0.5) +
  geom_jitter(width = 0.2, alpha = 0.3) +
  labs(
    x = "Study Group",
    y = "Daily Anxiety Frequency"
  ) +
  theme_minimal()

# B. QQ Plot 
p2 <- ggqqplot(df_clean, x = "daily_anxiety_frequency", facet.by = "study_group") +
  theme_minimal()

# Combine them
p1 + p2 + plot_annotation(tag_levels = 'A')

<Figure 3. Visualisation of anxiety levels and normality across study hour groups>

A. Boxplots with jitter comparing daily anxiety frequency between students who study more than 20 hours and those who study 20 hours or less.

B. QQ plots assessing the normality of anxiety scores within each group. The data approximately follows the diagonal line, supporting the assumptions of Welch’s t-test.

summary_tbl <- df_clean %>%
  group_by(study_group) %>%
  summarise(
    n = n(),
    Mean = mean(daily_anxiety_frequency, na.rm = TRUE),
    SD = sd(daily_anxiety_frequency, na.rm = TRUE)
  )

knitr::kable(summary_tbl, caption = "Table 1: Anxiety levels by Study Group")

Table 1: Anxiety levels by Study Group

study_group	n	Mean	SD
> 20 hrs	122	5.745902	2.383003
≤ 20 hrs	221	5.194570	2.340001

t.test(daily_anxiety_frequency ~ study_group, data = df_clean, var.equal = TRUE)

    Two Sample t-test

data:  daily_anxiety_frequency by study_group
t = 2.0753, df = 341, p-value = 0.03871
alternative hypothesis: true difference in means between group > 20 hrs and group ≤ 20 hrs is not equal to 0
95 percent confidence interval:
 0.02879255 1.07387046
sample estimates:
mean in group > 20 hrs mean in group ≤ 20 hrs 
              5.745902               5.194570 

1. Hypothesis

• Null hypothesis (\(H_0\)):
  There is no difference in anxiety levels between students who study more than 20 hours and those who study less.

• Alternative hypothesis (\(H_1\)):
  Students who study more than 20 hours per week report lower anxiety levels on average.

---

2. Assumptions

• Observations are independent

• Anxiety scores are approximately normally distributed within each study group

• Variances are equal(boxplot)

---

3. Test Static

• Test type: Two sample t-test

• Test statistic (t): 2.0753

• Degrees of freedom (df): 341

---

4. P-Value

• P-Value =0.03871

---

5. Decision

• Since the p-value(0.03871) is greater than 0.05, we accept the null hypothesis. This provides evidence that there are significant difference in anxiety_level between two study groups.

---

6. Conclusion

• Students who study more than 20 hours per week report significantly lower daily anxiety levels than those who studies less. While this association is statistically significant, the direction of casuality remains unclear and may be influenced by other unmeasured factors in student life.

---

2.3 Do early sleepers report lower anxiety levels than late sleepers?

df_clean <- df_clean %>%
  mutate(
    sleep_group = if_else(sleep_hour < 2 | sleep_hour >= 22, "Early", "Late")
  )
set.seed(2025)

# Make a working copy of anxiety and group labels
anx <- df_clean$daily_anxiety_frequency
grp <- df_clean$sleep_group

# Observed difference in mean anxiety
obs_diff <- mean(anx[grp == "Early"]) - mean(anx[grp == "Late"])

# Fast permutation test
n_sim <- 10000
perm_diffs <- replicate(n_sim, {
  shuffled_grp <- sample(grp)
  mean(anx[shuffled_grp == "Early"]) - mean(anx[shuffled_grp == "Late"])
})

# Two-sided p-value
p_val <- mean(abs(perm_diffs) >= abs(obs_diff))
p_val

[1] 0.458

library(tidyverse)

set.seed(2025)

# Define variables
anx <- df_clean$daily_anxiety_frequency
grp <- df_clean$sleep_group

# Calculate observed difference in mean anxiety (Early - Late)
obs_diff <- mean(anx[grp == "Early"]) - mean(anx[grp == "Late"])

# Permutation test
n_sim <- 10000
perm_diffs <- replicate(n_sim, {
  shuffled <- sample(grp)
  mean(anx[shuffled == "Early"]) - mean(anx[shuffled == "Late"])
})

# Calculate p-value (two-sided)
p_val <- mean(abs(perm_diffs) >= abs(obs_diff))

# Plot the null distribution with observed diff
perm_plot <- tibble(perm_diffs) %>%
  ggplot(aes(x = perm_diffs)) +
  geom_histogram(bins = 30, fill = "skyblue", color = "black") +
  geom_vline(xintercept = obs_diff, color = "red", linetype = "dashed", linewidth = 1.2) +
  annotate("text",
           x = obs_diff + 0.05,
           y = max(table(cut(perm_diffs, 30))) * 0.9,
           label = paste0("Observed diff = ", round(obs_diff, 3)),
           color = "red",
           hjust = 0,
           size = 4) +
  labs(
    title = "<Permutation Test: Difference in Mean Anxiety>",
    subtitle = paste0("p-value = ", round(p_val, 3)),
    x = "Mean difference (Early - Late sleepers)",
    y = "Frequency"
  ) +
  theme_minimal()

# print the finalized plot 
perm_plot

<Figure 4. Null distribution of mean anxiety differences between early and late sleepers, generated via 10,000 permutations. The red dashed line represents the observed difference in means (-0.194). Since the observed value lies well within the null distribution, the result is not statistically significant (p = 0.458).>

1. Hypothesis

• Null hypothesis (\(H_0\)): There is no difference in mean daily anxiety levels between early and late sleepers.

• Alternative hypothesis (\(H_1\)):
  There is a difference in mean daily anxiety levels between early and late sleepers.

---

2. Assumptions

• Observations of this are independent of each other.

• Anxiety scores are consistant among all the respondents those took survey.

---

3. Test Static

• Observed Difference(Early~Late): -0.194

This indicates that on average, early sleepers reported slightly lower anxiety(by 0.194 points) but this is very small.

---

4. P-Value

• P-Value = 0.458

This P-value conveys that there is 45.8% chance of observing difference in mean anxiety as extreme as -0.194 just by random chance, if null hypothesis is true. Since it is greater than 0.05(significance level), the result is not statistically significant.

---

5. Decision

• We failed to reject the null hypothesis.

---

6. Conclusion

• In conclusion, there is no strong statistical evidence that early sleepers and late sleepers experience different anxiety levels. While the observed difference suggests a slightly lower mean anxiety score for early sleepers, such difference is small and well within what we would expect by the chance alone. Hence, we can conclude that sleep time alone may not be a key factor in determining daily anxiety levels among students in this survey sample.

---

3 Final Conclusion

This report examined how daily anxiety levels relate to study habits, gender, and sleep patterns among DATA2X02 students at the University of Sydney. While the dataset was subject to selection and measurement biases due to it’s nature of self-reported, it still offered meaningful insights into student wellbeing.

This analysis produced three meaningful insights:

• 1. There was no significant association between gender and reported anxiety levels, suggesting that gender identity alone may not be a strong indicator of daily anxiety level.
• 2. Students who studied more than 20 hours per week reported significantly lower anxiety levels than those that studied less.
• 3. There was no significant difference in anxiety between early and late sleepers as through permutation resampling approach. While early sleepers showed slightly lower average anxiety score, the difference was not meaningfully large. This suggests that the bedtime alone is unlikely to explain difference in mental well-being(anxiety) within this survey sample.

In sum, these results suggests that academic workload may be closely related with student anxiety rather then demographic or behavioural lifestyle factors like gender or bedtime of university students. However, due to exploratory nature of analysis and limitations of datasets including small subgroup sizes, and potential reporting inaccuracies, caution must be taken when generalising these findings from this study.

Further studies could be built on these results by using more representative and larger samples, refining question phrasing to reduce measurement bias. In conclusion, understanding the behavioural patterns associated with anxiety is a crucial step toward to design effective student mental health support or aid.

4 References

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